Determine the intercepts of the line. $ -6x+3y=-7$ $x$ -intercept: $\Big($
Answer: The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}-6x+3\cdot{0}&=-7\\ -6x&=-7\\ x&=\dfrac{7}{6}\end{aligned}$ So the $x$ -intercept is $\left(\dfrac{7}{6},0\right)$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}-6\cdot{0}+3y&=-7\\ 3y&=-7\\ y&=-\dfrac{7}{3}\end{aligned}$ So the $y$ -intercept is $\left(0,-\dfrac{7}{3}\right)$. In conclusion, The $x$ -intercept is $\left(\dfrac{7}{6},0\right)$. The $y$ -intercept is $\left(0,-\dfrac{7}{3}\right)$.